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The corners of a sheet of paper are folded up to meet the opposite sides and (if the paper is not already square) the top is cut off, making a square sheet with diagonal creases. [ 1 ] The four corners of the square are folded into the center, forming a shape known in origami terminology as a blintz base or cushion fold. [ 2 ]
Arbitrary shapes, beyond symmetrical polyhedra, can also be constructed; a deltahedron with 2N faces and 3N edges requires 3N Sonobe modules. A popular class of arbitrary shapes consists of assemblies of equal size cubes in a regular cubic grid, which can be easily derived from the six unit cube by joining multiple ones at faces or edges.
A true 13×5 triangle cannot be created from the given component parts. The four figures (the yellow, red, blue and green shapes) total 32 units of area. The apparent triangles formed from the figures are 13 units wide and 5 units tall, so it appears that the area should be S = 13×5 / 2 = 32.5 units.
An Infinity cube made of dice being played with An animation showing different moves and states of the Infinity cube (click to animate) An Infinity cube is a kind of mechanical puzzle toy with mathematical principles. Its shape is similar to a 2×2 Rubik's cube. It can be opened and put back together from different directions, thus creating a ...
Modular origami or unit origami is a multi-stage paper folding technique in which several, or sometimes many, sheets of paper are first folded into individual modules or units and then assembled into an integrated flat shape or three-dimensional structure, usually by inserting flaps into pockets created by the folding process. [3]
Note that with the cube (see image) the perimeter of the resulting 2D drawing is a perfect regular hexagon: all the black lines have equal length and all the cube's faces are the same area. Isometric graph paper can be placed under a normal piece of drawing paper to help achieve the effect without calculation.
The fold-and-cut problem asks what shapes can be obtained by folding a piece of paper flat, and making a single straight complete cut. The solution, known as the fold-and-cut theorem, states that any shape with straight sides can be obtained. A practical problem is how to fold a map so that it may be manipulated with minimal effort or movements.
The Rubik's Cube caused an unprecedented boom of this category. A large number of variants have been produced. Cubes of dimensions from 2×2×2 to 33×33×33 have been made, as well as many other geometric shapes such as tetrahedral and dodecahedral. With a varying orientation of the axis of rotation a variety of puzzles with the same basic ...
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